Optical orthogonal codes (OOCs) were introduced by Salehi, as signature sequences to facilitate multiple access in optical fibre networks. The existence of optimal (υ,3,1)-OOCs had been solved completely. Although there are some partial results, the existence of optimal (υ, 4, 1)-OOCs is far from settled. In this letter, three general constructions for (υ, 4, 1)-OOCs via perfect difference families are presented, new infinite classes of (υ, 4, 1)-OOCs are then obtained.

R-regular Mth band filters are an important class of digital filters and are used in constructing Mth-band wavelet filter banks, where the regularity is essential. But this kind of filter has larger stopband peak errors compared with a minimax filter of the same length. In this paper, peak errors in stopband of R-regular 4th-band filters are reduced by means of superimposing two filters with successive regularities. Then the stopband peak errors in the resulting filters are compared with the original ones. The results show that the stopband peak errors are reduced significantly in the synthesized filter that has the same length as the longer one of the two original filters, at the cost of regularity.